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High-Coherence Electron and Ion Bunches from Laser-Cooled Atoms
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2014 J. Phys.: Conf. Ser. 488 012045
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XXVIII International Conference on Photonic, Electronic and Atomic Collisions (ICPEAC 2013) IOP Publishing
Journal of Physics: Conference Series 488 (2014) 012045
doi:10.1088/1742-6596/488/1/012045
High-Coherence Electron and Ion Bunches from
Laser-Cooled Atoms
A. J. McCulloch, D. V. Sheludko, C. T. Putkunz, S. D. Saliba, D. J.
Thompson, R. W. Speirs, D. Murphy, J. Torrance, B. M. Sparkes,
and R. E. Scholten
ARC Centre of Excellence for Coherent X-Ray Science, School of Physics, The University of
Melbourne, Australia
E-mail: [email protected]
Abstract. Cold atom electron and ion sources produce electron bunches and ion beams
by photoionisation of laser cooled atoms. They offer high coherence and the potential for
high brightness, with applications including ultrafast electron diffractive imaging of dynamic
processes at the nanoscale. Here we present our cold atom electron/ion source, with an electron
temperature of less than 10 K and a transverse coherence length of 10 nm. We also discuss
experiments investigating space-charge effects with ions and the production of ultra-fast electron
bunches using a femto-second laser. In the latter experiment we show that it is possible to
produce both cold and fast electron bunches with our source.
1. Introduction
Being able to image the dynamics of atomic-scale processes and produce a “molecular movie” is
the ultimate goal of x-ray and electron imaging [1]. This is motivated by a need to understand
critical phenomena underlying biology, materials sciences and technological applications. For
instance, rational drug design relies on knowing the molecular structure and function of certain
membrane proteins [2]. In a bid to achieve this goal many different technologies are being
developed. These include billion-dollar x-ray free electron lasers which attempt to produce
sufficient brightness in an x-ray beam for single-shot imaging of non-crystalline objects [3].
An alternative to creating very bright x-ray sources is to use electrons, where the sample
interaction is 104 to 106 times stronger [4], far fewer electrons are needed to achieve the same
results. The drawback to using electrons, however, is the space-charge effect; that is, the
Coulomb interaction within an electron bunch that dramatically reduces the source brightness
and coherence. This issue can be overcome if the electron bunch has a uniform ellipsoidal
distribution [5].
The ability to shape electron bunches into appropriate ellipsoidal distributions is one of the
motivations behind the development of a cold atom electron/ion source (CAEIS) [6]. Other
advantages of a CAEIS include the high source coherence due to the low temperatures of the
electrons and ions produced from the laser-cooled atoms and the promise of high brightness, with
up to 106 particles per bunch. Here we present an overview of our CAEIS, some investigation
of space-charge effects, and the creation of ultra-fast cold electron bunches.
Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution
of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
Published under licence by IOP Publishing Ltd
1
XXVIII International Conference on Photonic, Electronic and Atomic Collisions (ICPEAC 2013) IOP Publishing
Journal of Physics: Conference Series 488 (2014) 012045
doi:10.1088/1742-6596/488/1/012045
(a)
GND
–2000 V
(b)
Electron
bunches
Excitation
Imaging
detector
x
y
z
Photoionisation
beam (from behind)
Spatial light
modulator
2 mm
Trapping beams
Figure 1. (a) Experimental set-up of the cold atom electron/ion source. (b) False-colour image
of electron cloud detected on MCP. From Reference [8].
2. The Cold Atom Electron/Ion Source
2.1. Source of Cold Atoms
In our experiments we laser-cool and trap rubidium-85 atoms. We use an effusive oven to produce
hot rubidium, which is then cooled via a Zeeman slower before entering the trapping region.
This provides a high-flux source of slow atoms, and is described in more detail in Reference [7].
The atoms are then confined in a magneto-optic trap (MOT) located between two accelerator
plates, 55 mm apart. Using this method, up to 109 atoms can been trapped with a Gaussian
width of less than 1 mm, leading to densities up to 1011 cm−3 . The atom cloud temperature is
approximately 70 µK.
2.2. Creating Shaped Electron and Ion Bunches
To create electron and ion bunches, a two-stage ionisation process is used. Firstly, the trapping
and cooling lasers, as well as the magnetic fields of the MOT, are turned off. A pulse of laser
light resonant with the D2 F = 3 → F 0 = 4 transition (780 nm) is then directed onto the
atoms perpendicular the accelerator plates. This pulse is created by placing an acousto-optic
modulator in the path of a continuous wave (CW) laser and has a temporal width on the order of
microseconds. A 5 ns 480 nm pulsed laser beam is directed onto the excited atoms in a direction
parallel to the accelerator plates. The wavelength of the pulsed blue laser can be changed over
tens of nanometres to allow for either direct ionisation of the already-excited atoms, or to excite
them to a high-lying Rydberg state, where the static accelerator field induces field ionisation.
The pulsed blue laser is focused into a sheet of light at the MOT, with a full-width-halfmaximum width of approximately 150 µm. The 780 nm excitation laser profile, meanwhile, is
transformed into an arbitrary shape using a spatial-light modulator (SLM). This combination
of laser wavelengths and orientations creates the shaped electron and ion bunches, as shown in
Fig. 1(a). Approximately 105 electrons were produced in each bunch.
2.3. Detection
We select electrons or ions by appropriate choice of polarity for our accelerator front plates
(e.g. electrons in Fig. 1a). The electric field strength was approximately 40 kV/m. After constant
acceleration, the electrons or ions are propagated for 21.5 cm in a null field, then detected on
a microchannel plate detector (MCP) and imaged with a CCD camera to provide 2D spatial
2
XXVIII International Conference on Photonic, Electronic and Atomic Collisions (ICPEAC 2013) IOP Publishing
Journal of Physics: Conference Series 488 (2014) 012045
doi:10.1088/1742-6596/488/1/012045
(a)
3
Rb+
Derivative (10-2 μum-1)
T0 = 10 ± 5 K
Rydberg
5ns ionisation
480nm
2
5P
Shaped excitation
780nm
1
5S
0
-100
0
100
200
300
400
Excess ionisation energy (K)
(b)
(c)
(i)
1.0
0.8
Visibility
I n te g r a ti o n
(ii)
Intensity (a.u.)
(iii)
0.6
0.4
0.2
0
0
2
4
6
8
10
Distance (mm)
0
500
1000
Spatial frequency 1/d (m–1)
1500
12
Figure 2. (a) Electron bunch edge width. The error bars indicate one standard deviation over 30
shots, including statistical and systematic uncertainties. An upper limit to source temperature is
extracted by fitting Equation 1 to the data (solid line) with excess ionisation energy ∆Ec ≥ 0 K.
Inset shows the relevant energy levels and transitions in rubidium. From Reference [8]. (b)(i)
Desired excitation laser beam intensity profile used to create the SLM phase mask. (ii) Image
of resulting shaped electron bunch on MCP. (iii) Integrated line profile of the calculated fully
coherent electron distribution (red, dashed), the recorded electron image (blue points), and a
fit to the recorded data (red, solid). (c) Visibility of electron bunch pattern as a function of
spatial frequency, with a Gaussian fit to the visibility function resulting in Lc = 7.8 ± 0.9 nm.
The systematic uncertainty is measuring d was 3%. From Reference [11].
resolution of the bunch, as shown in Fig. 1b). Temporal evolution of the bunch can be determined
by monitoring the potential of the grounded component of the MCP.
2.4. Temperature and Coherence Length of Electrons Bunches
The temperature of the electron source can be determined by performing measurements of the
divergence of the bunches, which affects the edge acuity. The transverse thermal velocity of the
3
XXVIII International Conference on Photonic, Electronic and Atomic Collisions (ICPEAC 2013) IOP Publishing
Journal of Physics: Conference Series 488 (2014) 012045
doi:10.1088/1742-6596/488/1/012045
electron cloud determines the angular spread after propagation via the equation [9]
dQe
d1
= eκ
dr
2d1 + d2
s
eF
,
d1 (kB T0 + ∆E)
(1)
where Qe is the detector signal proportional to charge, r is the radial coordinate, e is the
electron charge, κ is linear magnification, d1 and d2 are the distances through which the bunch
is accelerated and freely propagated respectively, F is the accelerator field magnitude, kB is
Boltzmann’s constant, T0 is the minimum electron temperature, and ∆E is the excess energy of
the electrons after ionisation. By varying the excess energy given to the electrons (by changing
the wavelength of the blue laser) and fitting κ and T0 , the minimum temperature of the electrons
was found to be T0 < 10 ± 5 K [8]. The results are shown in Fig. 2(a). The electron temperature
is much higher than the cold atom temperature (70 µK) due to intrinsic heating processes
encountered during ionisation, such as disorder-induced heating.
From this minimum temperature we can determine the transverse coherence length of the
electron bunch via [10]
p
(2)
Lc = h̄/ me kB T0 ,
where me is the mass of the electron. Using the value for T0 obtained above gives Lc > 10±3 nm.
The arbitrary shaping ability of the CAEIS can also be used to directly measure the coherence
length. This was achieved by using a sinusoidally shaped excitation laser and measuring the
visibility of the electron pattern as a function of spatial frequency (Fig. 2b and 2c), resulting in
a measurement of Lc = 7.8 ± 0.9 nm [11]. A coherence length of 10 nm is already sufficient at
the source for imaging small biomolecules such as bacteriorhodopsin, where the unit cell length
is of order 10 nm. In contrast, photoemission electron sources with electron bunch temperatures
of order 104 K have an associated coherence length of 0.3 nm.
We have not yet measured the temperature of our ion bunches, but other groups have
measured temperatures on the order of milliKelvins, again limited by disorder-induced heating
[12].
3. Space-Charge Effects
Space-charge effects within clouds of electrons or ions cause bunch expansion. This is normally an
irreversible process and leads to a loss in coherence and brightness. However, if the bunch shape
is a uniform ellipsoid then the internal fields are linear, and though the bunch will still expand,
the expansion can be reversed by refocusing with conventional linear charged particle optial
systems, preserving the initial coherence and brightness of the source. It has been theoretically
shown that an initial bunch with a semi-circular transverse distribution and a very narrow
longitudinal distribution will evolve into a uniform ellipsoid [5].
Creating such a distribution experimentally is, however, quite challenging. The spatial
distribution of the initial bunch depends not only on the excitation beam profile, but also on
the initial density of the cold atom cloud, and the time-dependent behaviour of the excitation
process. We have simulated these effects using optical Bloch equations, and modelled the
evolution of the bunch shape using General Particle Tracer (GPT) simulations [13].
We have investigated space-charge effects using ions rather than electrons because they are
far more massive and slower, allowing for longer interaction times. The ion temperature is also
orders of magnitude lower than for electrons, so the effects of thermal diffusion are minimal.
In combination, the effects of Coulomb interactions within the bunch are much more clearly
discernible. Our investigations have led to the discovery of some interesting effects such as the
formation of density waves around an initially uniform circular ion bunch. This can be explained
by the formation of a diffuse halo of charges around the central core of the bunch. The halo is
created by re-absorption of spontaneous emission from the directly excited atoms. The dense
4
XXVIII International Conference on Photonic, Electronic and Atomic Collisions (ICPEAC 2013) IOP Publishing
Journal of Physics: Conference Series 488 (2014) 012045
doi:10.1088/1742-6596/488/1/012045
2 mm
(a)(i)
2 mm
(a)(ii)
(b)
3500
Emittance (nm rad)
3000
ps bunches
ns bunches
i
–Esp
ii
2500
2000
1500
1000
500
0
-15
-10
-5
0
5
10
15
20
25
30
35
40
Excess ionisation energy (meV)
Figure 3. (a) Typical pepperpot images used to extract the emittance of femtosecond-excited
CAEIS electron bunches. (i) A CCD image of the laser pulse used to excite the atoms. (ii)
Detected electron signal on MCP for an ionisation wavelength of 478.00 nm. (b) Measured
radial emittance as a function of excess ionisation energy. Each point represents 50 singleshot measurements with the error bars indicating one standard deviation combined from the
statistical deviation and systematic uncertainties. The dashed lines are theoretical plots. For
more information see Reference [16].
core then expands into the halo, due to space-charge repulsion, and creates a high-density
ring. We have also investigated the space-charge interaction of parallel beamlets to see the
influence of overlapping self-fields [14]. Our studies show good agreement between simulations
and experiments. The simulations reveal the sensitivity of the visibility of the high-density
features to the initial ion temperature: the structure is lost at temperatures of a few tens of
Kelvin, highlighting the advantages of the cold atom source in comparison with conventional
sources, which operate at room temperature or above, for studying these effects.
4. Ultra-Fast Cold Electrons
Ultra-fast electron diffraction enables the study of molecular structural dynamics with high
resolution at sub-picosecond timescales. This is important for understanding biochemical
dynamics such as protein folding and regulation, as well as the formation of cracks in novel
materials [4, 15]. Ultrafast exposure times will also allow high intensity imaging of radiation
sensitive samples, such as biologically relevant molecules, to obtain sufficient information about
the molecule before it dissociates, known as “diffract-before-destroy” imaging.
To achieve this with our CAEIS, we replaced the CW 780 nm excitation laser switched via
5
XXVIII International Conference on Photonic, Electronic and Atomic Collisions (ICPEAC 2013) IOP Publishing
Journal of Physics: Conference Series 488 (2014) 012045
doi:10.1088/1742-6596/488/1/012045
an acousto-optic modulator with a femto-second laser. With femtosecond excitation, the initial
electron pulse duration is limited by the spatial and temporal extent of the overlap between the
new femtosecond pulses and the 5 ns pulses of 480 nm light. The overlap produces a shaped
pulse of electrons or ions with a minimum duration of 150 ps [16].
The high bandwidth inherent to short laser pulses might be expected to increase the excess
energy spread of the electrons and thus destroy their transverse coherence. We performed an
emittance measurement using the pepperpot method. Instead of using a physical pepperpot, we
shaped the femto-second excitation as shown in Fig. 3(a)(i) and measured the spatial distribution
of the electron bunches at the MCP detector. By knowing the initial and final electron beamlet
distributions, the emittance εr can be calculated (for more details see Reference [16]). The
pepperpot measurements were performed for a series of different blue laser wavelengths, similar
to the temperature measurements discussed in Section 2, and compared to results with CW
excitation.
From the results (Fig. 3b) it can be seen that in Region (i) – i.e. just below the fieldfree ionisation threshold – the emittance increases, coinciding with an increase in ionisation
efficiency. In this region the electron bunches that are produced are both ultrafast, and still
highly coherent. In Region (i) the blue laser couples the 5P3/2 state to one or more fieldionising Rydberg states, resulting in an electron bunch with minimal spread. Above threshold, in
Region (ii), the emittance increases dramatically due to the opening of an alternative ionisation
pathway: when the energy of the ionisation laser is above threshold, the blue laser couples the
5P3/2 state directly to the continuum. In this case the large near-resonant bandwidth of the
780 nm femtosecond pulse substantially increases the energy spread. As the excess ionisation
energy increases further, a decrease in emittance is observed. This shows that the bandwidth of
the femtosecond laser is not contributing appreciably to the energy spread.
Below Region (i) the emittance is approximately constant (εr = 538 ± 26 nm), limited by
heating during the extraction process. In the same region, the emittance from the CW excitation
laser was 141 ± 7 nm. Though the femtosecond emittance is larger, the corresponding coherence
length is still relatively large for an electron source, at Lc = 4.0 ± 0.2 nm [16].
5. Conclusion
We have presented our cold atom electron/ion source, including characterisation of the electron temperature and coherence length. We have investigated the effect of space-charge on ion
bunches, including the formation of density waves due to spontaneous emission and reabsorption from the main interaction region. Finally we presented results showing that we can produce
ultra-fast (150 ps) electron clouds, while maintaining an coherence length of 4 nm. To improve
the emittance further we are looking to reduce the temperature by using Rydberg blockade
to overcome disorder-induced heating effects, and using our shaping ability to overcome spacecharge effects.
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XXVIII International Conference on Photonic, Electronic and Atomic Collisions (ICPEAC 2013) IOP Publishing
Journal of Physics: Conference Series 488 (2014) 012045
doi:10.1088/1742-6596/488/1/012045
[8] McCulloch, A J, Sheludko D V, Saliba S D, Bell, S C, Junker M, Nugent K A, and Scholten R E 2011 Nature
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7